A 10 micro faran capacitor is charged by a 30V dc supply & then connected across an uncharged capacitor of 50 micro faran. Calculate the(1) final potential difference across the combination & the (2)initial & final energies. How will you account for the difference in energies?

Capacitance on the charged capacitor C_{1}= 10μF = 10 x 10^{-6} F

Supply Voltage = 30V

Capacitance of an uncharged capacitor C_{2 }= 50μF = 50 x 10^{-6} F

When C_{2} is connected in the circuit the potential acquired by it is V_{2}

According to conservation of charge, initial charge on capacitor C_{1} is equal to final charge on capacitors C_{1} and C_{2} .

Therefore V_{2 }( C_{1}+ C_{2}) = C_{1}V_{1}

Substituting the values

V_{2 }= 5V

Initial energy of the system

E_{1} = ½ C_{1} V_{1}^{2}

E_{1} = 45 x 10^{-4} J

Electrostatic energy of the combination of two capacitors is given by:

E_{2} =1/2 (C1 + C2 ) V_{2}^{2}

E2 = 5 x 10^{-4} J

Hence the amount of electrostatic energy lost by the capacitor is

E= E_{1} – E_{2 }= 40 x 10^{-4} J

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